What is 3/27 plus 15/21? (Answer: 52/63)

Exact Answer

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Problem: What is 3/27 plus 15/21?
Formula / Expression: 3/27 + 15/21
Final Answer: 52/63
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 27 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 189 (which is smaller than their product 27 × 21 = 567, keeping the calculation simpler).
Working: LCD(27, 21) = 189

Step 2: Convert to Equivalent Fractions with Common Denominator 189
Multiply the numerator and denominator of 3/27 by 7, and multiply the numerator and denominator of 15/21 by 9 so both fractions share the common base 189.
Working: 3 × 7/27 × 7 = 21/189 and 15 × 9/21 × 9 = 135/189

Step 3: Add the Numerators
Now add the numerators (21 + 135 = 156) and keep the common denominator 189 unchanged.
Working: 21 + 135/189 = 156/189

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 156 and 189, which is 3. Divide both the numerator and denominator by 3.
Working: 156 ÷ 3/189 ÷ 3 = 52/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 52 by denominator 63 produces a repeating decimal (approximately 0.825397, or 82.5397%).
Working: 52 ÷ 63 = 0.825397 (82.5397%)

Key Values:
- Simplified Fraction: 52/63
- Mixed Number Form: 52/63
- Decimal Value: 0.825397
- Percentage: 82.5397%

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Solved with FractionsCalc:
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3/27 + 15/21 = 52/63

Simplified Fraction

52/63

Mixed Number

Proper (52/63)

Decimal Value

0.825397

Percentage

82.5397%

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Step-by-Step Solution: 3/27 + 15/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 27 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 189 (which is smaller than their product 27 × 21 = 567, keeping the calculation simpler).

LCD(27, 21) = 189

Step 2

Convert to Equivalent Fractions with Common Denominator 189

Multiply the numerator and denominator of 3/27 by 7, and multiply the numerator and denominator of 15/21 by 9 so both fractions share the common base 189.

3 × 7/27 × 7 = 21/189 and 15 × 9/21 × 9 = 135/189

Step 3

Add the Numerators

Now add the numerators (21 + 135 = 156) and keep the common denominator 189 unchanged.

21 + 135/189 = 156/189

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 156 and 189, which is 3. Divide both the numerator and denominator by 3.

156 ÷ 3/189 ÷ 3 = 52/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 52 by denominator 63 produces a repeating decimal (approximately 0.825397, or 82.5397%).

52 ÷ 63 = 0.825397 (82.5397%)

Visual Representation

The diagram below illustrates 3/27 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`52/63`
Mixed Number Form	`52/63`
Decimal Form	`0.825397`
Percentage	`82.5397%`

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Frequently Asked Questions

What is 3/27 plus 15/21 as a fraction?

3/27 + 15/21 in simplest fraction form is 52/63.

What is 3/27 plus 15/21 as a decimal?

3/27 + 15/21 converted to a decimal is 0.825397.

What is 3/27 plus 15/21 as a percentage?

3/27 + 15/21 expressed as a percentage is 82.5397%.

Does 3/27 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.825397...) because the denominator contains prime factors other than 2 and 5.